Laser interferometer gravitational wave detectors require the use of m
assive ultra-high-Q test mass pendulums to minimize thermal noise. The
verification of ultra-high Q-factors in pendulums is difficult due to
the coupling of support structure recoil losses into the pendulum sta
ge. We present a numerical analysis of three different pendulum suspen
sion systems to assess their performance. We show that conventional tw
o-stage and three-stage suspension systems cannot be expected to verif
y Q-factors beyond 10(8) due to recoil losses, but that a twin pendulu
m system can allow Q-factors of 10(10) to be observed.